Travian is a browser game that dont need any download, you can use it in any browsers, but choosing a right browser will give you more advantage than others. Sometimes you might need more than 1 browsers to make you play faster and to help you not to be caught easily when you play with scripts.
Why you need more than 1 browser? This will help you to play multiple accounts at the same time. I will share with you the guide on how to play more than one account using same browser, i will give in another post. You sometimes need to play multiple account if you are sitter or when you really want.
If you're using script, you also might need a 'clean'er browser so you can send your reports or igms or anything that you copy from your scripted browser to your alliance forums to hide that you using script in the game from others. You wouldn't know if your post will be detected by multihunter.
For scripted playing : you better use Mozilla FireFox. It can makes your gaming experience more exiting with tons of scripts to be try out.
For clean play : i recommend you to use Google Chrome since its the best faster browser available.
I advice you to stay away from Internet Explorer. It's a lame browser..slow and sometimes stupid (atleast,for me.)
p/s: I also know how to multiple your FireFox browser in another post some day. stay tuned.